NE461 Lecture Notes - Lecture 4: Fluid Mechanics, Newtonian Fluid, Clay Mathematics Institute

• School: University of Waterloo
• Department: Nanotechnology Engineering
• Course: NE461
• Professor: Juewen Liu

Document Summary

Lecture 4: governing equations for incompressible flow: conservation of mass: continuity equation. For incompressible fluids, conservation of mass is expressed as =0. is the velocity field. The divergence of flow is zero at any point in the flow. In vector calculus, divergence is a vector operator that measures the magnitude of a vector field"s source or sink at a given point. The divergence represents the volume density of the outward flux of a vector field from an infinitesimal volume around a given point. For example, if air is heated in a region it will expand in all directions such that the velocity field points outward from that region. Therefore the divergence of the velocity field in that region would have a positive value, as the region is a source. Example: show that any velocity field in 2d cartesian space defined by the stream function and. In a cartesian coordinate system, the divergence of a vector field =(cid:1847)(cid:2191)+(cid:1848)(cid:2192)+(cid:1849)(cid:2193) is.